# coding: utf-8

#  # Interacting with `sympy`
#  
# `pymbolic` can help take care of many *structural* transformations on your expression trees with great ease. Its main purpose is to help with program transformation after all, not to be a full computer algebra system. That said, if you need a full computer algebra system for things like calculus and simplification, it's easy to get your expressions converted between `pymbolic` and `sympy`:

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import sympy as sp
from pymbolic import var

x = var("x")
y = var("y")


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expr = (x**2 + 2*x + 1)/(x**2 + x)
print(expr)


# Let's import pymbolic's sympy interoperability code.

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# pymbolic.interop.sympy in newer versions of pymbolic
from pymbolic.sympy_interface import (
    PymbolicToSympyMapper, SympyToPymbolicMapper)

p2s = PymbolicToSympyMapper()
s2p = SympyToPymbolicMapper()


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sympy_expr = p2s(expr)
print(sympy_expr)


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sympy_result = sp.cancel(sympy_expr)
print(sympy_result)


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result = s2p(sympy_result)
print(result)


# One thing to note is that `PymbolicToSympyMapper` is a regular `pymbolic` mapper, and its behavior can be overridden in case something about the translation to sympy is not quite what you want.
# 
# `SympyToPymbolicMapper` also behaves very similarly (and can be overridden similarly) although it is not entirely the same kind of mapper.

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